Equation of a Line
Notes
is pronounced "x nought", and is pronounced "y nought", and so on
Vector Equation of a Line
We require 2 things to describe a line:
- A point
on the line - A vector
in the direction of the line (direction vector)
Direction vector
Definition
Position Vector Equation of a Line
Definition
Or
Or
Either way, same concept
Where:
is a position vector for a general point on the line is a position vector for a specific point on the line is a direction vector for the line where is a parameter
Parametric Equations
Examples
- Determine a vector equation of the line passing through
with the slope - State the parametric equations
- Determine other points on the line
- Sub non-zero values for
from vector equations
- Sub non-zero values for
- Check if a point is on the line
- Find value of
in the parametric equations, and if they are all equal, then the point is on the line
- Find value of
- Determine the direction vector for the line
use reduced form
- Determine the vector equation and the parametric equations of the following lines:
- The line
- The line parallel to the y-axis with the x-intercept of 2
- The line
, passing through the point and perpendicular to the line
- The line
Scalar Equation of a Line
Converting a Vector Equation of a Line to Standard Form